Preheat oven to 475°F
Prepare the compound butter by adding the butter, rosemary, thyme, garlic, and smoked paprika to a medium-sized bowl. Use a fork to fully incorporate the herbs, garlic, and paprika into the butter.
Pat the chicken dry with a paper towel. Liberally salt and pepper the cavity of the bird. Stuff the lemon halves and one sprig each of the rosemary and thyme into the cavity.
Use a spatula, or even better, your clean hands, to rub the butter mixture all over the outside of the bird. Wash hands and then sprinkle salt and pepper all over the outside of the chicken.
Place the chicken on a rack placed in a roasting pan breast-side up. Pour 1 cup of chicken broth into the pan.
Place in the oven and cook for 20 minutes, turning the pan 180° after 10 minutes, if browning too much on one side. Baste every 20 minutes. Add more chicken broth to the pan if becoming too dry or starting to burn.
Lower the heat to 400°F and cook until an internal temperature reaches 165°F. Continue basting every 20 minutes and adding more broth if necessary. (See Notes for Total Roast Time)
Remove the pan from the oven and carefully transfer the rack with the chicken on it to a cutting board. The chicken needs to rest for 10 minutes. Remove the lemons and herbs in the cavity before serving.
Meanwhile, pour off all but about 2 tablespoons of the liquid in the pan. Place the pan on the stove over two burners and heat to medium-high. Add the wine, broth, and a liberal pinch of salt and pepper and bring to a strong simmer. Cook for 2 minutes and then use a strainer to transfer the gravy/sauce into a heat-resistant gravy boat.
Place the roast chicken on a platter and serve at once with the gravy on the side.